# THE HARDEST GCSE MATHS QUESTION EVER?! (0.2% of students got it right)

TLDRThe video discusses the 'hardest GCSE maths question ever', which only 0.2% of students answered correctly. It explores the difficulty of translating diagrams and words into algebraic expressions, using the example of proving a relationship between the sides of two right-angled triangles with incremented lengths. The presenter solves the problem step by step, demonstrating the application of Pythagoras' theorem and algebraic manipulation, and concludes by explaining why it's impossible for all sides to be integers.

### Takeaways

- π² The video discusses a collection of extremely challenging GCSE maths questions that have been compiled over time.
- π The script highlights the low percentage of students who were able to answer these questions correctly, with some as low as 0.2%.
- π§ The presenter expresses surprise at the difficulty of the questions and the low success rates, suggesting that the questions are harder than they initially appear.
- π The script includes a specific example of a geometry problem involving right-angled triangles and the Pythagorean theorem.
- π€ The presenter attempts to solve one of the most difficult questions, which involves expanding and simplifying algebraic expressions.
- π The process of solving the problem requires translating the geometric information into algebraic equations and then simplifying them.
- π The presenter notes that only 0.2% of students were able to solve the final problem, which involves proving an algebraic identity.
- π The script demonstrates the importance of understanding algebraic manipulation and the application of the Pythagorean theorem to geometry problems.
- π€ The presenter explains that the key to solving these problems is to see the connection between the geometric diagram and the algebraic expressions.
- π« The script also includes a logical explanation of why a, b, and c in the problem cannot all be integers, based on the properties of integers and the presence of a 'half' in the equation.
- π¨βπ« The video concludes with the presenter suggesting that with proper tutoring and understanding of the concepts, one could be part of the 0.2% who solve such difficult questions.

### Q & A

### What is the main topic of the video script?

-The main topic of the video script is discussing a compilation of the hardest GCSE maths questions, including the percentage of students who got them right.

### What does the video script highlight about the GCSE maths questions?

-The video script highlights that some of the hardest GCSE maths questions have very low percentages of students getting them correct, with the lowest being 0.2%.

### What is the significance of the question with a 0.2% success rate?

-The question with a 0.2% success rate is considered extremely difficult, as only one in 500 students got it right. The video script explores why this might be the case.

### What common mistake do students make according to the video script?

-Students often mistakenly believe that (a + 1)^2 is the same as a^2 + 1, rather than correctly expanding it to a^2 + 2a + 1.

### How does the presenter explain the correct way to expand (a + 1)^2?

-The presenter explains that (a + 1)^2 should be expanded using the FOIL method, resulting in a^2 + 2a + 1.

### What mathematical concept does the presenter use to explain the difficulty of another question?

-The presenter uses Pythagoras' theorem to explain the difficulty of a question involving right-angle triangles.

### What does the presenter suggest is the reason students struggle with some questions?

-The presenter suggests that students struggle with questions that involve translating diagrams and English descriptions into mathematical expressions.

### What does the presenter conclude about the equation involving right-angle triangles?

-The presenter concludes that by expanding and simplifying the given equations, one can show that 2a + 2b + 1 equals 2c.

### Why does the presenter believe that not all values of a, b, and c can be integers?

-The presenter believes that not all values of a, b, and c can be integers because the expression a + b + 0.5 cannot be an integer if a and b are integers.

### What advice does the presenter give to students regarding these types of maths questions?

-The presenter advises students to learn the correct methods for solving these types of questions, suggesting that using an AI tutor could help them become part of the 0.2% who get the hardest questions right.

### Outlines

### π The Challenge of Difficult GCSE Exam Questions

The speaker discovers a document containing a compilation of notoriously difficult GCSE exam questions, along with the percentage of students who scored full marks on them. The document reveals that as the difficulty of the questions increases, the percentage of students who can answer them correctly decreases dramatically, with some questions having a success rate as low as 0.2%. The speaker expresses astonishment at these statistics and decides to tackle one of the most challenging questions, which involves mathematical concepts that many students find confusing, such as the difference between (a+1)^2 and a^2 + 1.

### π Translating Geometry to Algebra: A Right-Angle Triangle Puzzle

In this paragraph, the speaker delves into solving a particularly challenging geometry problem involving right-angled triangles. The problem requires showing that for two similar triangles with sides a, b, and c, the equation 2a + 2b + 1 = 2c holds true. The speaker uses the Pythagorean theorem to set up equations for both triangles and then manipulates these equations to derive the required relationship. The explanation highlights the difficulty students face in translating geometric diagrams into algebraic expressions and the process of simplifying these expressions to reach a solution. The speaker also addresses the additional challenge of proving that a, b, and c cannot all be integers, using logical reasoning based on the derived equation.

### π€ Reflecting on the Rarity of Correct Solutions and the Role of AI Tutors

The final paragraph reflects on the rarity of students being able to solve the complex problems presented in the document. The speaker suggests that with proper guidance, such as from an AI tutor, students could potentially become part of the small percentage who can correctly answer these questions. The speaker also invites viewers to share more challenging questions and expresses an interest in exploring even more difficult problems, hinting at the possibility of future videos on the topic. The paragraph concludes with a sign-off, indicating the end of the discussion.

### Mindmap

### Keywords

### π‘GCSE

### π‘Percentage of students

### π‘Constructed angle

### π‘Pythagoras

### π‘FOIL

### π‘Right-angled triangles

### π‘Algebra

### π‘Hypotenuse

### π‘Integers

### π‘AI Tutor

### Highlights

Document contains the hardest GCSE maths questions with the percentage of students who got full marks.

Only 10% of students answered a question on a constructed angle of 30 degrees correctly.

A question involving rearranging a formula was answered correctly by just 8.6% of students.

A probability question was only solved by 7% of students, indicating its difficulty.

A question about vectors and a regular hexagon was only answered correctly by 5.5% of students.

A question involving base, radius, height, and melting down to make a sphere was only solved by 2.4% of students.

A question on a solid cone in a solid hemisphere was only answered by 0.9% of students.

The last question in the document was only answered correctly by 0.2% of students.

The misconception that (a + 1) squared equals a squared + 1 is debunked using the FOIL method.

A challenge to solve a geometry problem involving right-angle triangles with measurements increased by 1.

Using Pythagoras' theorem to solve the problem of the triangles with increased measurements.

The realization that the problem can be simplified by removing c squared from both sides of the equation.

The conclusion that 2a + 2b + 1 equals c, derived from the simplified equation.

An explanation of why a, b, and c cannot all be integers in the context of the problem.

A demonstration that adding a half to an integer will never result in another integer.

The presenter's belief that with proper tutoring, students could be part of the 0.2% who solve these problems.

An invitation for viewers to share more challenging GCSE maths questions.